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If {:(f(x),=(e^(5x)-e^(2x))/(sin 3x),","...

If `{:(f(x),=(e^(5x)-e^(2x))/(sin 3x),",",x != 0),(,=k/2, ",",x = 0):}`
is continuous at x = 0, the value of k is

A

0

B

1

C

2

D

5

Text Solution

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The correct Answer is:
C
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TARGET PUBLICATION-CONTINUITY-Critical Thinking
  1. If f(x) is continuous at x = 0, where {:(f(x),=(8^(x)-2^(x))/(k^(x)-1)...

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  2. If f(x) is continuous at x=0, where f(x)=((e^(3x)-1)sin x^(@))/(x^(2))...

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  3. If {:(f(x),=(e^(5x)-e^(2x))/(sin 3x),",",x != 0),(,=k/2, ",",x = 0):} ...

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  4. If f(x) = (e^(x)-e^(sinx))/(2(x sinx)) , x != 0 is continuous at x = 0...

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  5. In order that the function f(x)=(x+1)^(cotx) is continuous at x = 0, f...

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  6. If {:(f(x),=((4x+1)/(1-4x))^(1/x),",",x != 0),(,=k, ",",x = 0):} is...

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  7. If {:(f(x),=(sec^2x)^(cot^2x),",",x != 0),(,=k, ",",x = 0):} is con...

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  8. If f(x) is continuous at x = (pi)/2, where f(x) = (sinx)^(1/(pi-2x)), ...

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  9. {:(f(x),=(log(1+kx))/(sin x),",",x != 0),(,=5, ",",x = 0):} If f is...

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  10. If {:(f(x),=(logx-log7)/(x-7),",",x != 7),(,=k, ",",x = 7):} is con...

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  11. If f(x) = {{:((log(1+2ax)-log(1-bx))/(x)",",x ne 0),(" "k",",...

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  12. {:(f(x),=((3^(sin x)-1)^(2))/(xlog(1+x)),",",x != 0),(,=k, ",",x = 0):...

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  13. The value of f(0) so that the function f(x) = (log(sec^2 x))/(x sin x)...

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  14. The value of a for which the function f(x)=f(x)={((4^x-1)hat3)/(sin(x...

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  15. f(x) ={((x^2-9)/(x-3)+a,",",x gt 3),(5, ",",x = 3),(2x^2+3x+b, ",",x l...

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  16. If f(x) is continuous at x = 0 , where f(x) ={(x^2+a,",",x ge 0),(2sqr...

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  17. Find the values of a and b sucht that the function f defined by ...

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  18. The value of p and q for which the function f(x) = {((sin(p+1)x+sinx...

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  19. If f(x) ={(e^(1/x),",","when"x != 0),(1,",","when"x = 0):} , then

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  20. If f(x) ={((x^(4)-16)/(x-2),",","when"x != 2),(16,",","when"x = 2):} ,...

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